Contrary to consensus protocols with predefined convergence based on time-varying gains as in [1]}, [2]}, [3]}, [4]}, [5]}, the proposed classes of protocols does not require the strong assumption of a common time-reference for all nodes. Moreover, unlike autonomous fixed-time consensus protocols [6]}, [7]}, which are based on a subclass of the fixed-time stable systems given in [8]}, which uses homogeneous in the bi-limit [9]} vector fields, in this paper a methodology for the design of new consensus protocols is presented, showing that predefined-time consensus can be achieved with a broader class of consensus protocols, that are not required to be homogeneous in the bi-limit. This result provides extra degrees of freedom to select a protocol, for instance, to reduce the slack between the predefined upper bound for the convergence and the exact convergence time. This methodology generalizes the recent results [6]}, [11]} on fixed-time consensus for dynamic networks formed by agents with first-order dynamics.
